I've been involved in a few video sharing situations in my time. At my last job, we actually had a city police department, university, and school district all sharing video, using two different recording platforms, and three different camera manufacturers. That was quite a time. I think the county emergency management department is going to be pulling all of the above into their own system this year, so that'll be another layer.
The simplest way, assuming the cameras are fixed, is just to add the cameras to each others' systems. I highly recommend using a second stream for this, though, because I've seen VMSs do strange things. Some will fight to keep settings set to what was configured in the admin tools for that system, others will simply accept what's on the camera. I've seen this do weird things to bitrate, frame rate, and more, and it's unpredictable. So keep the main stream to the home system, and send a second stream to the other.
If they're PTZ cameras, and you want to control them on the other system, it's harder. Adding a PTZ with tours and multiple operators to multiple systems is a nightmare. Some systems simply store the tour, presets, etc., in the camera, and trigger it from the VMS. Others explicitly tell the camera where to go, storing it in the VMS. Watch those two fight it out. It's comedy. (I actually had someone try to do this in production, and I shook my head from the time they mentioned it, all the way through implementation.) The option there is basically to add a video stream only, without PTZ control. This is often preferred, anyway, since the PTZ doesn't belong to the viewing entity, allowing them to control it could mess up operators of the main organization.